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Generalized hyperstability of the Jensen functional equation in ultrametric spaces. (English) Zbl 1394.39026
The author investigates some generalized hyperstability results for the Jensen functional equation \[ 2f\left(\frac{x+y}{2}\right)=f(x)+f(y) \] in ultrametric Banach spaces using the fixed point method derived by A. Bahyrycz and M. Piszczek [Acta Math. Hung. 142, No. 2, 353–365 (2014; Zbl 1299.39022)] and J. Brzdęk [Acta Math. Hung. 141, No. 1–2, 58–67 (2013; Zbl 1313.39037); Fixed Point Theory Appl. 2013, Paper No. 285, 9 p. (2013; Zbl 1297.39026)]. The author extends the results found by M. Almahalebi and A. Chahbi [Aequationes Math. 91, No. 4, 647–661 (2017; Zbl 1380.39025)].
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
47H10 Fixed-point theorems
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